Numerical Methods Using Java: For Data Science, Analysis, and Engineering

© Haksun Li, PhD 2022

H. Li, PhDNumerical Methods Using Javahttps://doi.org/10.1007/978-1-4842-6797-4_2

2. Linear Algebra

Haksun Li, PhD¹  

(1)

Hong Kong, China

 

Linear algebra algorithms are the most important algorithms in numerical computing. They are the foundation of all numerical algorithms. Many numerical algorithms, however complicated they are, involve some linear algebra computation. For example, a nonlinear problem is often difficult (or impossible) to solve directly. A popular technique is to approximate the nonlinear problem by multiple smaller linear (sub)problems (as in calculus). A linear problem then usually involves some vectors and matrices because of multiple variables. Vector and matrix arithmetic are ubiquitous in numerical computing. ...